In the present study, subgrid modeling schemes based on the concept of approximate inertial manifolds are derived in the framework of a quasigeostrophic multilayer model and their potentials and limits are investigated. The streamfunction field is decomposed into slow modes associated with large spatial scales and fast modes associated with small spatial scales. Based on a scale analysis of the terms in the equations of motion for the fast modes, an approximate nonlinear relationship between the slow and the fast variables is established; i. e. the subgrid scale motion is parametrised in terms of the resolvable scale motion. Physically, this reflects a balance of forces. Different decompositions of the flow field (in terms of spherical harmonics, normal modes or empirically determined patterns such as empirical orthogonal functions or principal interaction patterns) may be used. Moreover, various approximate inertial manifolds having different orders of accuracy are considered.
Reduced dynamical models resolving only the large scale motion explicitly and employing the subgrid modeling schemes described above are constructed. Their performance regarding short-term predictions as well as long-term integrations in comparison to a high-resolution spectral model is discussed.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics